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Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence TaoTue, 31 Mar 2015 18:04:26 +0000hourly1http://wordpress.com/By: Terence Taohttps://terrytao.wordpress.com/about/#comment-453384
Tue, 24 Mar 2015 02:16:05 +0000#comment-453384The Australian Mathematics Trust http://www.amt.edu.au/ may have some suitable programs or suggestions for this.
]]>By: Ronnie Brownhttps://terrytao.wordpress.com/about/#comment-453378
Mon, 23 Mar 2015 22:17:58 +0000#comment-453378The book “Men of Mathematics” by Bell records that the parents of the young Cauchy took advice on what mathematics he should be taught. That advice was that there was lots of time for maths, but he should be taught to write his own language! Look this up to see if I have got it right, and to what extent you agree!

You can also look at articles on popularisation on my web site. At Bangor we have run Masterclasses for selected 13 year olds and covered a variety of topics: spherical geometry, higher dimensions, knots. See also my presentation “Out of Line”.

I am a high school mathematics teacher in Australia, but have been recently working with an 8 year-old boy who is having mathematical discussions with me that go well beyond the Australian National Senior Curriculum.
I am in the process of trying to provide him with opportunities to be challenged in his mathematics (Senior Level) while still provide social and emotional connection with his peers. Do you have any advice or programs or resources that would be useful in ascertaining what the capabilities of this young boy are? His interests are so far beyond his age that I am sure there gaps in his understanding of mathematics if it were to be taught in a linear, scaffolded manner. I want to provide a focus and purpose to his mathematical studies, including filling in the gaps, without tempering his natural curiosity and interest to push the boundaries of what he is capable of understanding.

Any advice would be much appreciated.

Regards, Luke

]]>By: Robert Clarkhttps://terrytao.wordpress.com/about/#comment-452829
Mon, 09 Mar 2015 19:56:25 +0000#comment-452829Hello. Professor Tao. I am very impressed about your ability to make important contributions to very different fields of mathematics.
A question I’m interested in is the validity of climate models that show a large human contribution to global warming. These global climate models are quite complex mathematically. Perhaps you could offer some new insight into the validity of such models.

I hope you can read this comment and take this seriously enough to post about it.

Capablanca. H

]]>By: Samuel Chuhttps://terrytao.wordpress.com/about/#comment-447564
Tue, 30 Dec 2014 13:20:21 +0000#comment-447564Dear Prof Tao,
I observed one interesting prime factorization of the three consecutive numbers 2013, 2014 and 2015, 2013=3x11x61, 2014=2x19x53 and 2015=5x13x31, they are all factorized into three distinct primes. I guess there should be no other three consecutive numbers with this property but I can’t find a proof. What do you think?
]]>By: brianphilphttps://terrytao.wordpress.com/about/#comment-447027
Sat, 27 Dec 2014 16:14:25 +0000#comment-447027On twin primes: Many years ago, looking for heuristic evidence that there were infinitely many twin primes, I noticed that around 1 million there were 5 twin pairs with no primes in between. This surprised me as Sierpinski believed that anything that happened, happened early on in the natural numbers. A while ago I continued the search and come across an interval with 8 twin primes with no primes in between. The endpoints are: 1107819733063 to 1107819732823. Gaps with 5, 6 occur many times while 7 is rarer. I wonder if there are arbitrarily large such gaps.
]]>By: Bullsh!t Wikihttps://terrytao.wordpress.com/about/#comment-446908
Fri, 26 Dec 2014 14:34:31 +0000#comment-446908Dear professor Tao
I just wanted to say that this is an awesome blog about math. Learned a lot through it. Thank you.
I also wanted to ask you if you could add a link to my website on your link list. It is a free wiki about mathematical proof: http://proofs.wiki/.
Best regards, Brunner Nathan
]]>By: H. Schoenichhttps://terrytao.wordpress.com/about/#comment-446806
Fri, 26 Dec 2014 01:46:10 +0000#comment-446806How does one attach a Latex document?

I think the moderator should be able to review and cut and paste as much into a post as he/she likes. I have a hint for others, on a problem, but I don’t want to include the entirety of my hint, without a moderator making their own judgment — knowing of course that I have taken the time to write up the hint, in weighing how much of it will be passed along.

]]>By: H. Schoenichhttps://terrytao.wordpress.com/about/#comment-446187
Mon, 22 Dec 2014 07:23:45 +0000#comment-446187There is the challenge. The gauntlet thrown down. Not to be embarrassed, as a group, by a single mathematician, who in fact cares not a wit if he gets credit.

You say you want more than a hint, you want a full path laid out? Well, that is like a child asking for you to do his homework when you are the parent.

I will, however, try to help with the incentive structure if a specific, credible request is made by a group (of some defined nature, but not a group closed to new admitted). Some form of joint prize is likely to be necessary; how to ensure that the prize cannot be appropriate by a few is the trick.

As background motivational material, I do not want to see this happen, as recited by Prof. Godfeld at some length — and about which I have seen numerous similar, frankly silly, childish and egotistical attempts to gain individual credit for a process that yields results over time:

That two of the finest mathematicians between 1940 and 1980 should have had such a dispute is evidence of the extreme power of individual incentives, against the collective, unless a structure is put in place to harness those incentives.

One year; I conjecture I can do it in two if folk don’t start posting ideas to form a collective effort to do so, without free-rider incentives, and incentives for people to “cherry-pick” for self-aggrandizement, in blunt terms.

If the challenge is not accepted, I will, reluctantly given my other time commitments, step in and attempt to solve the Twin Prime Conjecture, which, without hints to you, I believe I can do given what I now know within no more than two years.

I look forward to notification that Prof Tao takes this seriously enough to post it as other than a mere comment.